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To test Ho: H= 107 versus H;: u#107 a simple random sample of size n= 35 is obtained. Complete parts a through e below. E Click here to view the t-Distribution Area in Right Tail. T-distribution area in right tail (a) Does the population have to be normally distributed to test this hypothesis? Why? O A. No, because n2 30. 1-1 B. Yes, because the sample is random. Area OC. Yes, because n2 30. JP 0.25 0.20 0.15 0.10 0,05 0.025 D. No, because the test is two-tailed. 1.000 1 376 1963 3078 6314 12 706 O O

To test Ho: H= 107 versus H;: u#107 a simple random sample of size n= 35 is obtained. Complete parts a through e below. E Click here to view the t-Distribution Area in Right Tail. T-distribution area in right tail (a) Does the population have to be normally distributed to test this hypothesis? Why? O A. No, because n2 30. 1-1 B. Yes, because the sample is random. Area OC. Yes, because n2 30. JP 0.25 0.20 0.15 0.10 0,05 0.025 D. No, because the test is two-tailed. 1.000 1 376 1963 3078 6314 12 706 O O

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Hypothesis Test: Population Mean **Scenario:** To test \( H_0: \mu = 107 \) versus \( H_1: \mu \neq 107 \), a simple random sample of size \( n = 35 \) is obtained. Complete parts a through b below: #### Question (a): Does the population have to be normally distributed to test this hypothesis? Why? - **A.** No, because \( n \geq 30 \). - **B.** Yes, because the sample is random. - **C.** Yes, because \( n \geq 30 \). - **D.** No, because the test is two-tailed. --- ### Explanation of T-Distribution Area in Right Tail The table provided is a t-distribution area chart showing critical values or t-scores for different degrees of freedom (df) and levels of significance in the right tail. The degrees of freedom are shown in the left-most column and repeated in the right-most column. Across the top are the different significance levels (0.25 to 0.0005) for the right tail. #### Key Points: - **Degrees of Freedom (df):** Calculated as \( n - 1 \), where \( n \) is the sample size. For the given scenario, df = 34. - **Significance Levels:** The columns (0.25, 0.20, 0.15, ..., 0.0005) represent the probability in the right tail. This is crucial for determining the critical value at which you would reject the null hypothesis. - **Critical Values:** For each df and significance level, there's a corresponding t-score. This t-score is compared to the calculated t-statistic from your sample to determine statistical significance. --- This resource is essential for conducting hypothesis tests involving small sample sizes or when the population standard deviation is unknown, necessitating the use of the t-distribution.
Transcribed Image Text:### Hypothesis Test: Population Mean **Scenario:** To test \( H_0: \mu = 107 \) versus \( H_1: \mu \neq 107 \), a simple random sample of size \( n = 35 \) is obtained. Complete parts a through b below: #### Question (a): Does the population have to be normally distributed to test this hypothesis? Why? - **A.** No, because \( n \geq 30 \). - **B.** Yes, because the sample is random. - **C.** Yes, because \( n \geq 30 \). - **D.** No, because the test is two-tailed. --- ### Explanation of T-Distribution Area in Right Tail The table provided is a t-distribution area chart showing critical values or t-scores for different degrees of freedom (df) and levels of significance in the right tail. The degrees of freedom are shown in the left-most column and repeated in the right-most column. Across the top are the different significance levels (0.25 to 0.0005) for the right tail. #### Key Points: - **Degrees of Freedom (df):** Calculated as \( n - 1 \), where \( n \) is the sample size. For the given scenario, df = 34. - **Significance Levels:** The columns (0.25, 0.20, 0.15, ..., 0.0005) represent the probability in the right tail. This is crucial for determining the critical value at which you would reject the null hypothesis. - **Critical Values:** For each df and significance level, there's a corresponding t-score. This t-score is compared to the calculated t-statistic from your sample to determine statistical significance. --- This resource is essential for conducting hypothesis tests involving small sample sizes or when the population standard deviation is unknown, necessitating the use of the t-distribution.
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